Suppose you were playing a game on your cell phone in which you were randomly given two rational expressions and were asked to identify the product of the two expressions. If one of the expressions were and the other expression were , would you be able to multiply them together? Could the product be simplified? In this Concept, you'll learn about the multiplication of rational expressions such as these.

### Guidance

Because a rational expression is really a fraction, two (or more) rational expressions can be combined through multiplication and/or division in the same manner as numerical fractions. A reminder of how to multiply fractions is below.

For any rational expressions ,

#### Example A

Multiply the following: .

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Solution:
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Simplify exponents using methods learned in previous Concepts.

#### Example B

Simplify .

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Solution:
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Multiplying Rational Expressions Involving Polynomials
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When rational expressions become complex, it is usually easier to factor and reduce them
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before
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attempting to multiply the expressions.

#### Example C

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Multiply
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Solution:
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Factor all pieces of these rational expressions and reduce before multiplying.

### Video Review

### Guided Practice

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Multiply
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Solution:
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Factor all pieces, reduce, and then multiply.

### Practice

Sample explanations for some of the practice exercises below are available by viewing the following video. Note that there is not always a match between the number of the practice exercise in the video and the number of the practice exercise listed in the following exercise set. However, the practice exercise is the same in both. CK-12 Basic Algebra: Multiplying and Dividing Rational Expressions (9:19)

In 1–10, perform the indicated operation and reduce the answer to lowest terms

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Mixed Review
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- Solve for and graph the solution on a number line: .
- What is true of any line parallel to ?
- Solve for .
- Graph and determine the domain and range: .
- Rewrite in vertex form by completing the square. Identify the vertex: .